From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6838 Path: news.gmane.org!not-for-mail From: Terry Bisson Newsgroups: gmane.science.mathematics.categories Subject: Re: a coalgebras over fields question. Date: Fri, 26 Aug 2011 01:57:12 +0000 (UTC) Message-ID: References: Reply-To: Terry Bisson NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1314385749 960 80.91.229.12 (26 Aug 2011 19:09:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 26 Aug 2011 19:09:09 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Fri Aug 26 21:09:05 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qx1m3-0005XO-Kp for gsmc-categories@m.gmane.org; Fri, 26 Aug 2011 21:09:03 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:34669) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qx1kf-0006s0-UW; Fri, 26 Aug 2011 16:07:37 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qx1kf-0006cL-80 for categories-list@mlist.mta.ca; Fri, 26 Aug 2011 16:07:37 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6838 Archived-At: Todd Trimble optonline.net> writes: >The finite-dim cocommutative > coalgebras over k coincide with the finitely presentable objects in > CocommCoalg_k, and the category of finite-dim cocommutative > coalgebras is dual to the category of finite-dim commutative > algebras/k. One concludes (a la Gabriel-Ulmer duality) that there > is an equivalence >=20 > CocommCoalg ~ Lex(CommAlg_{fd}, Set), >=20 > where the right side is the category of left exact functors on the > category of finite-dim commutative algebras/k. Hans-E. Porst pointed me to=20 similar results in his recent paper "On subcategories of the category of Hopf algebras",=C2=A0 Arabian Journal of Science and Enginering,=C2=A0(2011), DOI 10.1007/s13369-011-00= 90-4=20 Others recommended his article "On corings and comodules",=20 Archivum Mathematicum 42 (2006), no. 4, 419-425.=20 Preprints of these are available at http://www.math.uni-bremen.de/~porst/ I am finding these comments very helpful. Thanks greatly, Terry Bisson [For admin and other information see: http://www.mta.ca/~cat-dist/ ]